Identifying critical mass in the global cellular telephony market

Abstract

Technology diffusion processes are often said to have critical mass phenomena. We apply a model of demand with installed base effects to provide theoretically grounded empirical insights about critical mass. Our model allows us to rigorously identify and quantify critical mass as a function of installed base and price. Using data from the digital cellular telephony market, which is commonly assumed to have installed base effects, we apply our model and find that installed base effects were generally not strong enough to generate critical mass phenomena, except in the first cellular markets to introduce the technology.

Introduction

Successful new technologies and innovations typically diffuse in an S-shape. While the focus of past research has often been on the inflection point of a diffusion curve where diffusion slows down after a period of rapid growth, it is arguably just as important to identify the point on the diffusion curve when a technology starts penetrating the mass market. Different literatures have called this phenomenon “product takeoff” (Agarwal and Bayus, 2002, Golder and Tellis, 1997, Lee et al., 2003), a “catastrophe” (Cabral, 1990, Cabral, 2006), a “punctuated equilibrium” (Loch and Huberman, 1999) or “critical mass” (Cool et al., 1997, Evans and Schmalensee, 2010, Mahler and Rogers, 1999, Markus, 1987). We focus on the last and derive conditions for the existence of critical mass before identifying it empirically in the global cellular telephony market.

What, then, is critical mass? A common definition is that at critical mass “diffusion becomes self-sustaining” (Rogers, 2003: 243). This is qualitatively different to most conventional technology diffusion processes that rely on heterogeneous consumers and price decreases and/or quality increases (Grajek and Kretschmer, 2009, Loch and Huberman, 1999). Critical mass phenomena rely on a rapidly evolving endogenous process over time, e.g. installed base effects driving diffusion even in the absence of price decreases. The link between technology diffusion and installed base effects is well established (Cabral, 1990, Cabral, 2006, Granovetter, 1978, Kretschmer, 2008, Markus, 1987, Rohlfs, 1974), and research identifying multiple stable equilibria separated by an unstable one (Economides and Himmelberg, 1995, Evans and Schmalensee, 2010, Katz and Shapiro, 1985) characterizes the transition from one equilibrium to the other as critical mass.

We adapt the model by Cabral (1990) to develop a simple structural demand model of a non-durable good or service with installed base effects. We use the logic of multiple equilibria and endogenous diffusion outlined above to show that critical mass — a self-sustaining diffusion process — will only emerge if boundary conditions on the strength of installed base effects, the size of the installed base, and the current market price, are met. We find that these three parameters are substitutes in terms of reaching critical mass: for stronger network effects, critical mass is reached for higher prices and lower installed bases; for a higher installed base, network effects can be weaker and prices higher for critical mass to still exist; and so on. We estimate demand in the global cellular telephony industry between 1998 and 2007 and find that demand for cellular services displayed critical mass phenomena only in pioneering markets.

Our paper makes two contributions to the economics of technology diffusion: First, we operationalize and test the model by Cabral (1990) empirically, offering a simple but rigorous formal test for identifying critical mass, i.e. whether a technology displays periods of endogenous and rapid diffusion. We show that the critical mass point depends on price given that sufficiently strong installed base effects exist in a market. Our approach is complementary to work focusing on the adoption dynamics of durable goods with indirect network effects (Dubé et al., 2010, Gowrisankaran and Stavins, 2004, Ohashi, 2003). Our work also complements simulation models on industry dynamics and transitions (Lee et al., 2003, Loch and Huberman, 1999) as we derive information about demand conditions and especially the strength of installed base effects in real-life markets which can help calibrate simulation models. Our empirical model has two key advantages: (i) it imposes modest data requirements and (ii) it gives a linear (in parameters) diffusion equation with fixed effects, which is convenient to work with empirically.

Second, we show for the case of digital cellular telephony that critical mass was a local rather than a global phenomenon. That is, we find critical mass only in markets that pioneered the technology, i.e. that started offering 2G services early. Our empirical results suggest that critical mass is a function of both installed base and price, the latter being more important. Specifically for pioneering markets, we find that cellular telephony would have “taken off” without any installed base at an average price of 36 US cents per minute. However critical mass is reached at a slightly higher price (38 US cents) when the installed base of subscribers is about 24% of the population, suggesting that installed base can only substitute for the “right” price to some extent.